It is a truth universally acknowledged that the available, sociable, and genuinely attractive man is a character highly in demand in social settings. Dinner hosts are always looking for the man who fits all the criteria. When they don't find him (often), they throw up their hands and settle for the sociable but unattractive, the attractive but unsociable, and, as a last resort, for the merely available.
The shortage of appealing men is a century-plus-old commonplace of the society melodrama. The shortage—or—more exactly, the perception of a shortage—becomes evident as you hit your late 20s and more acute as you wander into the 30s. Some men explain their social fortune by believing they've become more attractive with age; many women prefer the far likelier explanation that male faults have become easier to overlook.
The problem of the eligible bachelor is one of the great riddles of social life. Shouldn't there be about as many highly eligible and appealing men as there are attractive, eligible women?
Actually, no—and here's why. Consider the classic version of the marriage proposal: A woman makes it known that she is open to a proposal, the man proposes, and the woman chooses to say yes or no. The structure of the proposal is not, "I choose you." It is, "Will you choose me?" A woman chooses to receive the question and chooses again once the question is asked.
The idea of the woman choosing expressed in the proposal is a resilient one. The woman picking among suitors is a rarely reversed archetype of romantic love that you'll find everywhere from Jane Austen to Desperate Housewives. Or take any comic wedding scene: Invariably, it'll have the man standing dazed at the altar, wondering just how it is he got there.
Obviously, this is simplified—in contemporary life, both sides get plenty of chances to be selective. But as a rough-and-ready model, it's not bad, and it contains a solution to the Eligible-Bachelor Paradox.
You can think of this traditional concept of the search for marriage partners as a kind of an auction. In this auction, some women will be more confident of their prospects, others less so. In game-theory terms, you would call the first group "strong bidders" and the second "weak bidders." Your first thought might be that the "strong bidders"—women who (whether because of looks, social ability, or any other reason) are conventionally deemed more of a catch—would consistently win this kind of auction.
But this is not true. In fact, game theory predicts, and empirical studies of auctions bear out, that auctions will often be won by "weak" bidders, who know that they can be outbid and so bid more aggressively, while the "strong" bidders will hold out for a really great deal. You can find a technical discussion of this here. (Be warned: "Bidding Behavior in Asymmetric Auctions" is not for everyone, and I certainly won't claim to have a handle on all the math.) But you can also see how this works intuitively if you just consider that with a lot at stake in getting it right in one shot, it's the women who are confident that they are holding a strong hand who are likely to hold out and wait for the perfect prospect.
This is how you come to the Eligible-Bachelor Paradox, which is no longer so paradoxical. The pool of appealing men shrinks as many are married off and taken out of the game, leaving a disproportionate number of men who are notably imperfect (perhaps they are short, socially awkward, underemployed). And at the same time, you get a pool of women weighted toward the attractive, desirable "strong bidders."
Where have all the most appealing men gone? Married young, most of them—and sometimes to women whose most salient characteristic was not their beauty, or passion, or intellect, but their decisiveness.